Question

Solve
$\frac{1}{2}\int \frac{(-4+2x)}{\sqrt{5-4x+x^2}}$

Answer 1

$\frac{1}{2}\int \frac{(-4+2x)}{\sqrt{5-4x+x^2}}dx$

Let, $5-4x+x^2=t$

$⟹(-4+2x)dx=dt$

$⟹\frac{1}{2}\int \frac{dt}{\sqrt{t}}$

$⟹\frac{2\sqrt{t}}{2}+C$

$⟹\sqrt{5-4x+x^2}+C$